From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Re: functions Omega->Omega
Date: Mon, 14 Jul 1997 20:25:22 -0300 (ADT) [thread overview]
Message-ID: <Pine.OSF.3.90.970714202504.11822B-100000@mailserv.mta.ca> (raw)
Date: Mon, 14 Jul 1997 14:24:43 -0400
From: Philip J. Scott <scpsg@matrix.cc.uottawa.ca>
>Date: Fri, 11 Jul 1997 16:56:25 -0400 (EDT)
>From: Andre Scedrov <scedrov@saul.cis.upenn.edu>
>
>
> > f(a) & a = f(true) & a
> >
> > I wonder whether anyone has noticed this formula before?
>
>Similar formulas and their analogs in intuitionistic second-order
>propositional calculus are discussed in my paper in the Annals Pure
>Appl. Logic 27 (1984) 155-164. That paper was motivated by Higgs's
>observation that every monic Omega -> Omega in a topos is an involution,
>see Peter Johnstone's paper "Automorphisms of Omega" in Alg. Universalis
>9 (1979) 1-7.
>
> Andre Scedrov
For a logical proof of Higgs' theorem, based on the above observations
of Scedrov, see Lambek-Scott (Introd. to Higher Order Cat. Logic), p.160,
Exercise 4. A further result along these lines is in Lemma 12.3, p. 190 of
our book.
Phil Scott
next reply other threads:[~1997-07-14 23:25 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
1997-07-14 23:25 categories [this message]
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1997-07-12 17:55 categories
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